A method for the solution of the homogeneous inventory-production optimisation problem

  • 1 Institute of Automatic Control and Information Technology, Faculty of Electrical Engineering and Computer Science, Cracow University of Technology


The subject of this paper is the inventory-production problem, which is a one of the optimization problems in a decision area in which inventory volume and production volume are considered together. There are many approaches to this problem but for the first time, this problem is modelled by means of a capacitated graph network and a solution to the problem is proposed on the basis of this model which consists of finding the maximum flow with the minimum sum of production and inventory cost. In this article, only a solution for one kind of product for the deterministic inventory-production optimisation problem is presented and for this one kind of product, a maximum flow with a minimum cost for each considered demand period is calculated. The maximum flow with minimum cost is a solution to the homogenous inventory-production optimisation problem. The solution to the one kind of product for the inventory-production problem consist of maximum flow with minimum cost for a total demand from all periods, which has been taken into consideration.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Al-Khenhairi A. (2010). Optimal control of a production inventory system with generalized exponential distributed deterioration. Journal of Mathematical Sciences: Advances and Applications, 4(2), 395–411.

  • Baten A., Kamil A. (2011). Optimal Production Control in Stochastic Manufacturing Systems with Degenerate Demand. East Asian Journal on Applied Mathematics, 1(1), 89–96.

  • Baten A., Kamil A. (2009). Analysis of inventory-production systems with Weibull distributed deterioration. International Journal of Physical Sciences, 4(11), 676–682.

  • Baten A., Kamil A. (2010). Optimal control of a production inventory system with generalized Pareto distributed deterioration items. Journal of Applied Sciences, 10(2), 116–123.

  • Bayındıra Z.P., Birbilb S.I., Frenk J.B.G. (2007). A deterministic inventory/production model with general inventory cost rate function and piecewise linear concave production costs. European Journal of Operational Research, 179, 114–123.

  • Bensoussan A. (2011). Dynamic programming and inventory control. Amsterdam: IOS Press.

  • Bhowmick J., Samanta G.P. (2011). A Deterministic Inventory Model of Deteriorating Items with Two Rates of Production, Shortages, and Variable Production Cycle. International Scholarly Research Network ISRN Applied Mathematics, ID 657464.

  • Bounkhel M., Tadj L., Benhadid Y. (2005). Optimal control of a production system with inventory-level-dependent demand. Applied Mathematics E-Notes, 5, 36–43.

  • Chaudhary K., Singh Y., Jha J. (2013). Optimal Control Policy of a Production and Inventory System for multi-product in Segment Market. Mathematica, 25, 29–46.

  • El-Gohary A., Elsayed A. (2008). Optimal Control of a Multi-Item Inventory Model, International Mathematical Forum. 3(27), 1295–1312.

  • Emamverdi G.A., Karimi M.S., Shafiee M. (2011). Application of Optimal Control Theory to Adjust the Production Rate of Deteriorating Inventory System. Middle-East Journal of Scientific Research, 10(4), 526–531.

  • Olanrele O., Kamorudeen A., Adio T.A. (2013). Application of Dynamic Programming Model to Production Planning, in an Animal Feedmills. Industrial Engineering Letters, 3(5), 9–17.

  • Rad M., Khoshalhan F. (2011). An integrated production-inventory model with backorder and lot for Lot Policy. International Journal of Industrial Engineering & Production Research, 22(2), 127–134.

  • Read E.G., George J.A. (1990). Dual Dynamic Programming for Linear production/inventory systems. Computer Math. Applications, 19(11), 29–42.

  • Samanta G., Roy A. (2004). A Deterministic inventory model of deteriorating items with two rates of production and shortages. Tamsui Oxford Journal of Mathematical Sciences, 20(2), 205–218.

  • Yanl K., Kulkarni K.V. (2008). Optimal inventory policies under stochastic production and demand rates. Stochastic Models, 24, 173–190.


Journal + Issues